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Answer :
We know that for collinear points area of triangle = 0 ,i.e.,
\( 0 \ = \frac{1}{2}[x_1(y_2 - y_3) \ + \ x_2(y_3 - y_1) \ + \ x_3(y_1 - y_2)] \)
(i) \( 7(1-k) + 5(k+2) + 3(-2-1) \ = \ 0 \)
=> \( 7 - 7k + 5k + 10 - 9 \ = \ 0 \)
=> \( 2k \ = \ 8 \)
=> \( k \ = \ 4 \)
(ii) \( 8(-4+5) + k(-5-1) + 2(1+4) \ = \ 0 \)
=> \( 8 - 6k + 10 \ = \ 0 \)
=> \( 6k \ = \ 18 \)
=> \( k \ = \ 3 \)